1. Field of the Invention
The present invention relates generally to the field of quantum information processing, and more specifically to efficient quantum computation.
2. Related Art
Quantum computation (QC), including photonic QC, has received significant attention in recent years. Initial work on photonic QC considered different circuit-based approaches. In the circuit-based QC paradigm, including circuit-based photonic QC, computation is effected by transforming an input state into an output state by applying a suitable sequence of logic gates, comprising a computational circuit, to quantum computational units known as qubits (derived from quantum bits). An example of such a logic gate is a CNOT gate. The CNOT gate is paradigmatic of a type of gate that is required in quantum computation, in which the qubits can be made to become entangled with each other. (Entanglement is a uniquely quantum mechanical phenomenon that plays a crucial role in quantum computation.) Such a logic transformation (i.e., a gate) can only be realized by using a mechanism by which qubits interact.
Photonic QC utilizes particular quantum states of photons as qubits. From a hardware perspective, photons are easy to move around in optical fiber, making the use of (states of) photons as qubits more convenient in this sense than other choices of physical realizations of qubits. The choice of photons as qubits motivated the choice of nonlinear Kerr-type media in the first analyses of photonic QC, as discussed in the article by Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, in Phys. Rev. Lett., 75:4710 (1995), which is incorporated by reference in its entirety. Although this approach in principle enables photonic entangling gates, practical difficulties associated with the use of Kerr-type media made this method problematic.
Interest in photonic QC was renewed with the appearance of the work of Knill, Laflamme and Milburn (KLM), as described in the article by E. Knill, R. Laflamme, G. J. Milburn, in Nature (London) 409:46 (2001), which is incorporated by reference in its entirety. This approach makes use of linear optics, combined with measurements carried out on ancillary photons, in order to circumvent the difficulties associated with the use of nonlinear media. Although it avoids the use of nonlinear media, the KLM approach to linear optics quantum computation (LOQC) is nevertheless problematic due to the inefficiency associated with the necessity of dealing with extremely large numbers of ancillary photons, as discussed in the article by M. A. Nielsen, in Phys. Rev. Lett. 93:040503 (2004), which is incorporated by reference in its entirety.
Both the non-linear approach and the linear approach in photonic QC are formulated within the circuit-based paradigm. An alternative to the circuit-based approach is a cluster-based approach that evolved later. A cluster comprises multiple entangled qubits, constructed in such a way as to enable universal quantum computation, effected solely by suitable measurements performed on the constituents of the cluster. Cluster states are discussed in several references, such as R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86:5188 (2001), R. Raussendorf, D. E. Browne, and H. J. Briegel, Phys. Rev. A 68:022312 (2003), H. J. Briegel and R. Raussendorf, Phys. Rev. Lett., 86:910, (2001), all of which are incorporated herein by reference in their entireties. With the discovery of the cluster-based paradigm, the possibility of using photons as the nodes in a cluster was explored.
Note that both circuit-based and cluster-based paradigms are unified in a framework provided by G. Gilbert et al. in “A Theory of Physical Quantum Computation: The Quantum Computer Condition”, quant-ph/0507141), which is incorporated by reference in its entirety.
It has been observed that a photonic cluster may furnish a more efficient realization of a quantum computation than a photonic circuit if certain techniques from LOQC were used to build the photonic cluster (as opposed to directly executing the computation itself), as discussed in the article by M. A. Nielsen in Phys. Rev. Lett. 93:040503 (2004), which is incorporated by reference in its entirety. Daniel E. Browne and Terry Rudolph refined this idea, and presented a more efficient scheme for the construction of photonic clusters in the article titled “Resource-Efficient Linear Optical Quantum Computation”, published in Phys. Rev. Lett. 95:010501 (2005), which is incorporated by reference in its entirety.
In Browne and Rudolph's scheme, the suggestion of Nielsen to use LOQC-derived operations to construct a cluster is replaced by a proposal to use simpler “fusion” operations to construct a cluster. However, while type-I fusion operations are relatively cost-effective, Browne and Rudolph also require use of resource-costly type-II fusion operations, leaving room for the exploration of a more efficient cluster construction method.
Note that a number of additional methods for constructing clusters have been suggested, for example, in the articles by L. M. Duan, R. Rausendorff, in Phys. Rev. Lett., 95, 080503 (2005), and by Q. Chen, J. Cheng, K. L. Wang, J. Du, in Phys. Rev. A, 73, 012303 (2006), both of which are incorporated by reference in their entireties. Additionally, small photonic cluster states have been experimentally implemented, as reported, for example, in the articles by P. Walther et al, in Nature 434:169 (2005), by N. Kiesel, C. Schmidt, U. Weber, O. Guhne, G. Toth, R. Ursin, H. Weinfurter, in Phys. Rev. Lett. 95:210502 (2005), and by A-N. Zhang, C-Y. Lu, X-Q. Zhou, Y-A. Chen, Z. Zhao, T. Yang, and J-W. Pan, in Phys. Rev. A, 73, 022330 (2006), all of which are incorporated herein by reference in their entireties. However, none of the references provide an efficient method for creating building block clusters for universal quantum computation, where the clusters are formed using minimal number of intermediate transformation steps.
Thus, what is needed is an improved method for efficiently constructing generic quantum computational clusters, including but not limited to, photonic clusters, as building blocks for universal quantum computation so as to minimize the use of resources.